Method and apparatus for acquiring wide-band pseudorandom noise encoded waveforms

ABSTRACT

The method and apparatus of the present invention is directed to architectures for signal processing, such as for performing analog-to-digital and digital-to-analog conversions, in which the source signal is decomposed into subband signals by an analysis filter, processed, and the processed subband signals combined to form a reconstructed signal that is representative of the source signal.

[0001] The present application claims priority from U.S. ProvisionalApplication Ser. Nos. 60/087,036 filed May 28, 1998; 60/056,455 filedAug. 21, 1997; and 60/056,228 filed Aug. 21, 1997, all of which areincorporated herein by this reference.

FIELD OF THE INVENTION

[0002] The present invention relates generally to a method and apparatusfor acquiring wide-band random and pseudorandom noise encoded waveformsand specifically to a method and apparatus for acquiring wide-bandsignals, including deterministic signals, random signals andpseudorandom noise encoded waveforms that divides the waveform into aplurality of subbands prior to signal processing thereof.

BACKGROUND

[0003] Analog-to-digital converters are devices that convert real worldanalog signals into a digital representation or code which a computercan thereafter analyze and manipulate. Analog signals representinformation by means of continuously variable physical quantities whiledigital signals represent information by means of differing discretephysical property states. Converters divide the full range of the analogsignal into a finite number of levels, called quantization levels, andassigns to each level a digital code. The total number of quantizationlevels used by the converter is an indication of its fidelity and ismeasured in terms of bits. For example, an 8-bit converter uses 2⁸ or256 levels, while a 16-bit converter uses 2¹⁶ or 65536 levels.

[0004] During the conversion process, the converter determines thequantization level that is closest to the amplitude of the analog signalat that time and outputs the digital code that represents the selectedquantization level. The rate at which the output is created indicatesthe speed of the converter and is measured in terms of samples persecond (sps) or frequency in Hertz (Hz). As will be appreciated, alarger number of bits and therefore quantization levels equates into afiner representation of the analog signal.

[0005] In designing an analog-to-digital converter, there are a numberof considerations. In many applications for example it is desirable thatthe converter has not only a high rate of speed but also a large numberof quantization levels or a high degree of fidelity. Such converters aredifficult to build and therefore tend to be highly complex and veryexpensive. The key reason is that conversion errors and theconsequential device layout constraints for reducing such errors, bothof which can be ignored at slow speeds, can become significant at highspeeds. As a result, in existing converters, high fidelity and highspeed are commonly mutually exclusive; that is, the higher the converterspeed the lower the converter fidelity and vice versa.

SUMMARY OF THE INVENTION

[0006] It is an object of the present invention to provide ananalog-to-digital converter that has a high fidelity and a high speed.Related objectives are to provide such an analog-to-digital converterthat is relatively simple and inexpensive.

[0007] The present invention is directed to a method and apparatus forprocessing signals, particularly wide-band signals, includingdeterministic signals, random signals, and signals defined bypseudorandom waveforms with a relatively high degree of fidelity andefficiency at a high speed and at a low cost. The invention isparticularly useful for processing wideband signal, including signalsdefined by broadband signals (i.e., signals having a bandwidth ofpreferably more than about 1 kHz and more preferably more than about 1GHz).

[0008] The signal can be in any suitable form such as electromagneticradiation, acoustic, electrical and optical.

[0009] In one embodiment, the method includes the following steps:

[0010] (a) decomposing the analog or digital signal into a plurality ofsignal segments (i.e., subband signals), each signal segment having asignal segment bandwidth that is less than the signal bandwidth;

[0011] (b) processing each of the signal segments to form a plurality ofprocessed signal segments; and

[0012] (c) combining the processed signal segments into a compositesignal that is digital when the signal is analog and analog when thesignal is digital. As will be appreciated, the sum of the plurality ofsignal bandwidths is approximately equivalent to the signal bandwidth.The means for processing the signal segments can include any number ofoperations, including filtering, analog-to-digital or digital-to-analogconversion, signal modulation and/or demodulation, object tracking, RAKEprocessing, beamforming, null steering, correlation,interference-suppression and matched subspace filtering.

[0013] In a particularly preferred application, the signal processingstep (b) includes either analog-to-digital or digital-to-analogconversions. The use of signal segments rather than the entire signalfor such conversions permits the use of a lower sampling rate to retainsubstantially all of the information present in the source signal.According to the Bandpass Sampling Theorem, the sampling frequency ofthe source signal should be at least twice the bandwidth of the sourcesignal to maintain a high fidelity. The ability to use a lower samplingfrequency for each of the signal segments while maintaining a highfidelity permits the use of a converter for each signal segment that isoperating at a relatively slow rate. Accordingly, a plurality ofrelatively inexpensive and simple converters operating at relativelyslow rates can be utilized to achieve the same rate of conversion as asingle relatively high speed converter converting the entire signal withlittle, if any, compromise in fidelity.

[0014] The means for decomposing the signal into a number of signalsegments and the means for combining the processed signal segments toform the composite signal can include any number of suitable signaldecomposing or combining devices (e.g., filters, analog circuitry,computer software, digital circuitry and optical filters). Preferably, aplurality or bank of analog or digital analysis filters is used toperform signal decomposition and a plurality or bank of analog ordigital synthesis filters is used to perform signal reconstruction. Theanalysis and synthesis filters can be implemented in any number of waysdepending upon the type of signal to be filtered. Filtration can be by,for example, analog, digital, acoustic, and optical filtering methods.By way of example, the filters can be designed as simple delays or verysophisticated filters with complex amplitude and phase responses.

[0015] In a preferred configuration, a plurality or bank of analysisand/or synthesis filters, preferably designed for perfectreconstruction, is used to process the signal segments. As will beappreciated perfect reconstruction occurs when the composite signal, oroutput of the synthesis filter bank, is simply a delayed version of thesource signal.

[0016] In one configuration, the analysis filters and synthesis filtersare represented in a special form known as the Polyphase representation.In this form, Noble identities are can be used to losslessly move thedecimators to the left of the analysis filters and the interpolators tothe right of the synthesis filters.

[0017] In another configuration, noise components in each of the signalsegments can be removed prior to signal analysis or conversion in theprocessing step. The removal of noise prior to analog-to-digitalconversion can provide significant additional reductions incomputational requirements.

[0018] In yet another configuration, a coded signal is acquired rapidlyusing the above-referenced invention. In the processing step, the signalsegments are correlated with a corresponding plurality of replicatedsignals to provide a corresponding plurality of correlation functionsdefining a plurality of peaks; an amplitude, time delay, and phase delayare determined for at least a portion of the plurality of peaks; and atleast a portion of the signal defined by the signal segments isrealigned and scaled based on one or more of the amplitude, time delay,and phase delay for each of the plurality of peaks.

[0019] In another embodiment, a method is provided for reducing noise ina signal expressed by a random or pseudorandom waveform. The methodincludes the steps of decomposing the signal into a plurality of signalsegments and removing a noise component from each of the signal segmentsto form a corresponding plurality of processed signal segments. Themeans for decomposing the signal can be any of the devices noted above,and the means for removing the noise component includes a noise reducingquantizer, noise filters and rank reduction. Signal reconstruction mayor may not be used to process further the processed signal segments.This embodiment is particularly useful in acquiring analog signals.

[0020] In yet a further embodiment, a method is provided for combining aplurality of signal segments (which may or may not be produced byanalysis filters). In the method, synthesis filtering is performed oneach of the plurality of signal segments. The means for performingsynthesis filtering can be any of the devices noted above.

[0021] A number of differing system configurations can incorporate thesynthesis filtering means in this embodiment of the invention. Forexample, a system can include, in addition to the synthesis filteringmeans, means for emitting the plurality of signal segments from aplurality of signal sources (e.g., antennas); means for receiving eachof the plurality of signal segments (e.g., antennas); and means forconverting each of the signal segments from analog format to digitalformat (e.g., analog-to-digital converter).

[0022] In another configuration, the system includes: a plurality ofanalysis filters to decompose a source signal into a plurality ofdecomposed signal segments; a plurality of digital-to-analog conversiondevices for converting the plurality of decomposed signal segments fromdigital into analog format to form a corresponding plurality of analogsignal segments; a plurality of amplifiers to form a correspondingplurality of signal segments; a plurality of signal emitters foremitting the plurality of signal segments; and a plurality of receptorsfor receiving the plurality of signal segments.

[0023] In yet another configuration, the system includes: a plurality ofanalysis filters to decompose a source signal into a plurality ofdecomposed signal segments; a plurality of amplifiers to amplify thedecomposed signal segments to form a corresponding plurality of signalsegments; a plurality of signal emitters for emitting the plurality ofsignal segments; and a plurality of receptors for receiving theplurality of signal segments.

[0024] In another embodiment, a method is provided in which digitalsignals are decomposed, processed, and then recombined. Signalprocessing can include signal correlation (e.g., signal modulation ordemodulation), and oblique projection filtration (e.g., as described incopending U.S. Patent Application Ser. No. 08/916,884 filed Aug. 22,1997, entitled “RAKE Receiver For Spread Spectrum Signal Demodulation,”which is incorporated herein fully by reference).

BRIEF DESCRIPTION OF THE DRAWINGS

[0025]FIG. 1 depicts a first embodiment of the present invention;

[0026]FIG. 2 depicts an analog signal;

[0027]FIG. 3 depicts the analog signal of FIG. 2 divided up into aplurality of signal segments;

[0028]FIG. 4 depicts the first embodiment including decimation;

[0029]FIGS. 5A and 5B depict noble identities;

[0030]FIG. 6 depicts a polyphase filter representation;

[0031]FIG. 7 depicts a polyphase filter representation with nobleidentities;

[0032]FIG. 8 depicts another embodiment of the present invention;

[0033]FIG. 9 depicts the quantization process of the quantizers in FIG.8;

[0034]FIG. 10 depicts a subband digital transmitter;

[0035]FIG. 11 depicts a subband analog transmitter;

[0036]FIG. 12 depicts a subband receiver;

[0037]FIG. 13 depicts rank reduction for noise filtering;

[0038]FIG. 14 depicts another embodiment of the present invention;

[0039]FIG. 15 depicts another embodiment of the present invention;

[0040]FIG. 16 depicts RAKE processing;

[0041]FIG. 17 depicts a multiplexed radar transmitter architecture;

[0042]FIG. 18 depicts a radar receiver architecture;

[0043]FIG. 19 depicts a digital communications example of a recursive,adaptive Wiener filter;

[0044]FIG. 20 depicts an alternative RAKE processing methodology; and

[0045]FIG. 21 depicts a least squares, multiple input multiple outputfilter design problem.

DETAILED DESCRIPTION

[0046] Referring to FIG. 1, an embodiment of the present invention isillustrated. As can be seen from FIGS. 1 and 2, a wideband, pseudorandomor random signal 40 (shown in FIG. 2) is passed to a bank or pluralityof analysis filters 44 a-n. The signal 40 has a frequency band ordomain, F_(s), having frequency bounds, f_(o), (lower) and f_(n),(upper), and therefore a bandwidth of f_(o)-f_(n) (FIG. 2). Thebandwidth commonly is at least about 1 kHz, more commonly at least about1 GHz. Each of the analysis filters 44 a-n pass only a portion of thefrequency band of the signal to form a plurality of subband signals 48a-n, or time frequency components, characterized by discrete portions ofthe frequency band, F_(s), of the signal 40 (FIG. 3). As will beappreciated, the summation of the individual frequency bandwidths of allof the subband signals 48 a-n is substantially the same as the bandwidthof the signal 40 (FIG. 3). The various subband signals 48 a-n areprocessed 52 a-n independently as described below to form acorresponding plurality of processed signal segments 56 a-n. Theprocessed signal segments 56 a-n are passed to a bank or plurality ofsynthesis filters 60 a-n and combined to form a composite signal 64.Generally, the signal 40 is analog or digital and, when the signal 40 isanalog, the composite signal 64 is digital, and, when the signal 40 isdigital, the composite signal 64 is analog.

[0047] The analysis and synthesis filters 44 a-n and 60 a-n can be inany of a number of configurations provided that the filters pass onlydiscrete, or at most only slightly overlapping, portions of thefrequency domain of the signal 40. It is preferred that the frequencybands of the subband signals overlap as little as possible. Preferably,no more than about 5% and more preferably no more than about 1% of thefrequency bands of adjacent subband signals overlap.

[0048] The filters can be analog or digital depending on the type ofsignal 40 or the processed signal segments 56 a-n. Examples of suitableanalog analysis and synthesis filters include a suitably configuredbandpass filter formed by one or more low pass filters, one or more highpass filters, a combination of band reject and low pass filters, acombination of band reject and high pass filters, or one or more bandreject filters. Digital analysis and synthesis filters are typicallydefined by software architecture that provides the desired filterresponse.

[0049] In a preferred configuration shown in FIG. 4, the signal 40 isdecomposed by the analysis filter bank 46 (which includes analog ordigital analysis filters Hk(z) 44 a-n) into subband signals which areeach sampled by a downsampler 64 a-n performing an M-fold decimation(i.e., taking every M^(th) sample), and the sampled subband signals arefurther sampled after signal processing by an up-sampler 68 a-n (and/orexpander (which fills in L-1 zeros in between each sample)) and thefurther sampled subband signals are combined by a synthesis filter bank62 (that includes analog or digital synthesis filters Gk(z) 60 a-n). Thesampled subband signals, denoted by x₀(n), x₁(n), . . . x_(m−1)(n), arethe outputs of the N-band analysis filter bank and the inputs to theN-band synthesis filter bank. As a result of decimation, the subbandsignals are 1/N the rate of the input rate of the signal 40.

[0050] Preferably, the analysis and synthesis filters are perfectreconstruction filters such that the composite signal 64 is a delayedversion of the signal 40 (i.e., y(n)=u(n−L) where y(n) is the compositesignal, u(n) is the signal, and L is time of delay). Using perfectreconstruction filters, the subband signals 48 a-n can be downsampledwithout any loss in fidelity of the output signal. This downsampling ispermissible because the subband signals are of narrow bandwidth and theconsequence of the downsampling is that any processing application 52a-n that is embedded in the subbands can run at significantly reducedrates.

[0051] As will be appreciated, a perfect reconstruction filter systemcan be formed by a number of different methods, including quadraturemirror filter techniques. A preferred technique for designing a filterbank is known as a least squares multiple input multiple output filterdesign notation. According to this technique, which is illustrated inFIG. 21, a rational transfer matrix defining one of the filter banks isknown, i.e., either H(z) or G^(T)(z), along with a rational transfermatrix F(z) defining the ideal output of the filter banks. Assuming thatH(z) and F(z) are the known rational transfer matrices, the unknownrational transfer matrix, G^(T)(z), is determined by the followingequation:

G ^(T)(z)=[F(z) U ^(T)(Z ⁻¹)]+H₀ ⁻¹(Z)

[0052] where

[0053] H(z)=H₀(z)U(z); [H₀(z) is the minimum phase equivalent of H(z)]

[0054] U(z)U^(T)(z⁻¹)=I; Paraunitary

[0055] [F(z)U(z⁻¹)]_(x): Causal part of F(z)U^(T)(z⁻¹)

[0056] As will be appreciated if G^(T)(z) were known and H(z) wereunkown, then the equation would be solved for H(z) rather than G^(T)(z),and G^(T)(z) would be decomposed into the following:

G^(T)(z)=G_(o) ^(T)(z)U(z)

[0057] where

[0058] G_(o) ^(T)(z) is the minimum phase equivalent of G^(T)(z).

[0059] In a preferred embodiment, the rational transfer matrices of theanalysis and/or synthesis filters are mathematically expressed in apolyphase filter representation. Exemplary equations defining thedecomposition of the signal 40 by the analysis filters 44 a-n includethe following:${H(z)} = {\sum\limits_{l = 0}^{M - 1}{z^{1}{E_{l}\left( z^{M} \right)}}}$

[0060] where

[0061] M is the number of subbands (which is the same as the number ofanalysis filters in the analysis filter bank; l is the subbanddesignation);${E_{l}\left( z^{M} \right)} = {\sum\limits_{n = {- \infty}}^{\infty}{{e_{l}(n)}\quad z^{- n}}}$e_(l)(n) = h(M  n + l), 0 ≤ l ≤ M − 1

[0062] (known as a Type 1 polyphase filter representation) and${H(z)} = {\sum\limits_{l = 0}^{M - 1}{z^{- {({M - 1 - l})}}{R_{l}\left( z^{u} \right)}}}$

[0063] where

R_(l)(z^(M))=E_(M−1−l)(z)

[0064] (known as Type 2 polyphase filter representation). As will beappreciated, other techniques exist for expressing a rational transfermatrix defining a filter system including impluse response and filterdescription.

[0065] Noble identities can be used to losslessly move the decimators tothe left of the analysis filters and the L-fold up-sampler and/orexpander to the right of the synthesis filters. In this manner, theanalysis and synthesis filters operate on lower rate data, therebyrealizing significant computational savings. The noble identitiesinclude:

[0066] Identity I: Decimation by M followed by filtering defined by themathematical function H(z) is equivalent to filtering by H(z^(M))followed by decimation by M (FIG. 5A).

[0067] Identity II: Filtering by G(z) followed by an upsampling by L isequivalent to upsampling by L followed by filtering by G(z^(L)) (FIG.5B).

[0068] By way of example, assume H(z) defines an order N finite impulseresponse (FIR) digital analysis filter with impulse response h(n), M=2,u(n) is the source signal and X(n) is the subband signal. Using the type1 polyphase representation above, H(z) is decomposed to yield thefollowing:

H(z)=H _(o)(z ²)+H ₁(z ²)

[0069] Based on the foregoing, FIG. 6 is a polyphase representationbased implementation of H(z) without noble identities and FIG. 7 is apolyphase representation-based implementation of the analysis filtersH(z) using noble identities to move the decimators ahead of the analysisfilters. In this configuration, H_(o)(z²) and H₁(z²) are FIR filters oforder n_(o)+1 and n₁+1, where N=n_(o)+n₁+1. H_(o)(z²) and H₁(z²) operateat half the rate as compared to H(z) and therefore have two units oftime in which to perform all the necessary computations, and thecomponents are continually active (i.e., there are no resting times).Accordingly, there is an M-fold reduction in the number ofmultiplications and additions per unit of time when using both polyphaserepresentation and the noble identities to implement an M-folddecimation filter.

[0070] Subband signal processing can take a variety of forms. In oneembodiment shown in FIG. 8 which depicts a receiver and antennaarchitecture, the source signal 40 and subband signals 48 a-n are inanalog form and a plurality of quantizers or analog-to-digitalconverters are used to convert the subband signals 48 a-n to digitalform before further processing 82 (e.g., correlation for encoded subbandsignals, subband signal digital beamforming in multiple antenna systems,etc.) and/or synthesis of the digital subband signals 78 a-n isperformed. As noted above, the subband signals 48 a-n are preferablysampled by each of the decimators or downsamplers 64 a-n at a rate of atleast about twice the bandwidth of the corresponding subband signal 48a-n to maintain fidelity. As shown in FIG. 9, each quantizer, oranalog-to-digital converter, 74 a-n determines the digital word orrepresentation 90 a-n that corresponds to the bin 86 a-n havingboundaries capturing the amplitude of the analog subband signal at thattime and outputs the digital word or representation that represents theselected quantization level assigned to the respective bin. The digitalsubband signals 78 a-n are converted 94 a-n from radio frequency (RF) tobase band frequency and optionally subjected to further signalprocessing 60. The processed subband signals 98 are formed into adigital composite signal 102 by the synthesis filter bank 60.

[0071] To provide increased accuracy, noise rejecting quantizers can beutilized as the quantizers 74 a-n. As will be appreciated, a noiserejecting quantizer assigns more bits to the portions of the subbandsignal having less noise (and therefore more signal) and fewer bits tothe noisy portion. This selective assignment is accomplished byadaptively moving the bin boundaries so as to narrow the bin width(thereby increasing quantization fidelity. An example of a designequation for a Lloyd-Max noise rejecting quantizer is as follows:${t_{k} = {\frac{x_{k - 1} + x_{k}}{2} + \frac{{\delta^{2}\left( x_{k} \right)} - {\delta^{2}\left( x_{k - 1} \right)}}{2\left( {x_{k} - x_{k - 1}} \right)}}};{x_{k} = {e_{k} - {\frac{1}{2}\quad \frac{{\delta^{2}\left( x_{k} \right)}}{x_{k}}}}}$

[0072] where:

[0073] x is the signal to be quantized;

[0074] N is the number of quantization levels;

[0075] k is signal identifier;

[0076] σ is the noise covariance.

[0077] The mean squared quantization error (MSE) ξ² is as follows:$\xi^{2} = {{E\left( {x - \hat{x}} \right)}^{2} = {E_{x}^{2} + {\sum\limits_{k = 0}^{N - 1}{\left\lbrack {{\sigma^{2}\left( x_{k} \right)} + x_{k}^{2} - {2x_{k}e_{k}}} \right\rbrack \quad P_{k}}}}}$

[0078] where:

[0079] {x_(k)}_(o) ^(N−1) are the representation points;

[0080] {c_(k)}_(o) ^(N−1) are the quantization bins;

[0081] {t_(k)}_(o) ^(N−1) are the bin thresholds;

[0082] f_(y)(y) is the probability density function of y;

[0083] y=x+n, where x is the signal component and n the noise component;e_(k) = E    x|y ∈ C_(k)] = 1/P_(k)∫_(t_(k))^(t_(k + 1))E[x|y = α]  fy(α)  α; andP_(k) = P[y ∈ C_(k)] = ∫_(t_(k))^(t_(k + 1))fy(α)  α

[0084] The LM equations require that the bin thresholds be equidistantfrom the representation points and that each representation point be theconditional mean of x in the corresponding quantization bin. As will beappreciated, a Lloyd-Max (LM) quantizer substantially minimizes the meansquared error between the discrete approximation of the signal and itscontinuous representation.

[0085] The noise covariance, δ, can be estimated by linear mean squarederror estimation techniques. Linear mean squared error estimates arecharacterized by the following equation:

{circumflex over (X)}=Ty=R_(xy)R_(yy) ⁻¹y

[0086] where T is the Wiener filter, R_(xy) is the cross covariancebetween x and y and R_(yy) is the covariance of y.

[0087] R_(xy) and R_(yy) are unknown and require estimation. A number oftechniques can be used to estimate R_(xy) and R_(yy), including anadaptive Wiener filter (e.g., using the linear mean squared algorithm),direct estimation, sample matrix inversion and a recursive, adaptiveWiener filter, with a recursive, adaptive Wiener filter being morepreferred.

[0088] The recursive, adaptive Wiener filter is explained in Thomas, J.K., Canonical Correlations and Adaptive Subspace Filtering, Ph.DDissertation, University of Colorado Boulder, Department of Electricaland Compute Engineering, pp.1-110, June 1996. which is incorporatedherein by reference in its entirety. In a recursive, adaptive Wienerfilter assume {circumflex over (T)}_(M) denotes the filter when Mmeasurements of X and Y are used. Then {circumflex over (T)}_(M) is theadaptive Wiener filter

T_(M)=X_(M)Y_(M)*(Y_(M)Y_(M)*)⁻¹={circumflex over (R)}_(xy){circumflexover (R)}_(yy) ⁻¹,

X_(M)=[x₁x₂ . . . x_(M)]; X_(M)=[x_(M)x]

Y_(M)=[y₁y² . . . y_(M)]; Y_(M)=[y_(M)y]

[0089] If another measurement of x and y is taken, and one more columnis added to X_(M) and Y_(M) to build {circumflex over (T)}_(M−1):

{circumflex over (T)} _(M+1) =X _(M) Y _(M) *{circumflex over (R)}_(M+1) ⁻¹ +xy*{circumflex over (R)} _(M−1) ⁻¹

[0090] The estimate of _(M+1) is {circumflex over (X)}_(M+1)

{circumflex over (X)}_(M+1)={circumflex over (T)}_(M+1)Y_(M+1)

[0091] Using the estimate of X_(M+1), one can read off {circumflex over(x)}_(M+1), which is the estimate of x:${\hat{x}}_{M + 1} = {{\frac{1}{1 + r^{2}}{\overset{\sim}{x}}_{M}} + \frac{r^{2}}{1 + r^{2}}}$

[0092] where

[0093] r²=y*{circumflex over (R)}_(M) ⁻¹y and {tilde over(x)}_(M+1)={circumflex over (T)}_(M)y.

[0094] Based on the above, when one observes y, the best estimate of theunknown x is {tilde over (x)}, with corresponding estimation error{tilde over (E)}_(M+1) and covariance {tilde over (Q)}_(M+1). If theunknown x becomes available after a delay, then {tilde over (x)}_(M+1)can be updated to {circumflex over (x)}_(M+1) with error covariance{tilde over (E)}_(M+1) and covariance {tilde over (Q)}_(M+1). The twocovariances are related by the following formula:${\overset{\sim}{Q}}_{M + 1} = {{\hat{Q}}_{M + 1} + {\frac{r^{2}}{1 + r^{2}}x\quad x^{*}}}$

[0095] By way of example and as illustrated in FIG. 19, consider adigital communication application in which the modulation schemeinvolves transmitting x₀ and x₁ when bits 0 and 1 are to be sent. Duringthe setup of the communication link, the transmitter sends a known bitsequence across the unknown channel. Let X_(M) be the matrix of signalsthat correspond to the known bit sequence. The receiver observes Y_(M),which is the channel filtered and noise corrupted version of X_(M).Since the receiver knows the bit pattern, and therefore X_(M), it isable to build {circumflex over (T)}_(M). Therefore we refer to X_(M) andY_(M) as the training set.

[0096] Once the communication link is established, the transmitter sendsa signal x, which corresponds to a data bit. The receiver observes thecorresponding y and uses it to estimate x using {circumflex over(T)}_(M):

{tilde over (x)}={circumflex over (T)}_(M)y

[0097] The receiver determines r², cos²θ and sin²θ.

[0098] When cos²θ is approximately equal to 1, {tilde over (x)} isdeemed to be a good estimate of x and is used to decide if a 1 or 0 wassent. If, however, cos²θ<<1, then the estimate {tilde over (x)} isscaled by cos²θ, as required by equation 14, before it is used to decideif a 1 or 0 was sent. Once the decision of 1 or 0 is made, the true x isknown and can be used to build {tilde over (x)} as required by equation14 above and as illustrated in FIG. 19. The x and y are also added tothe training set to update {circumflex over (T)}_(M).

[0099] In another embodiment, the source signal 40 is digital and theanalysis filters are therefore digital, signal processing is performedby a digital-to-analog converter, and the synthesis filters are analog.FIG. 10 depicts a subband digital transmitter according to thisembodiment. The signal 100 is in digital format and is transmitted to abank of analysis filters 104 a-n to form a plurality of digital subbandsignals 108 a-n; the digital subband signals 108 a-n are processed bydigital-to-analog converters 112 a-n to form analog subband signals 116a-n; the analog subband signals 116 a-n are amplified by amplifiers 120a-n to form amplified subband signals 124 a-n; and the amplified subbandsignals 124 a-n transmitted via antennas 128 a-n.

[0100] In another embodiment shown in FIG. 11, a subband analogtransmitter is depicted where the signal 140 is analog and not digital.The signal 140 is decomposed into a plurality of analog subband signals144 a-n by analog analysis filters 148 a-n and the analog subbandsignals 144 a-n amplified by amplifiers 152 a-n, and the amplifiedsubband signals transmitted by antennas 156 a-n.

[0101] In yet another embodiment shown in FIG. 12, a subband receiver isdepicted that is compatible with the subband analog transmitter of FIG.11. Referring to FIG. 12, a plurality of subband signals 160 a-n arereceived by a plurality of antennas 164 a-n, the received subbandsignals 168 a-n down converted from radio frequency to basebandfrequency by down converters 172 a-n; the down converted subband signals176 a-n which are in analog form are converted by quantizers 180 a-nfrom analog to digital format; and the digital subband signals 184 a-ncombined by synthesis filters 188 a-n to form the digital compositesignal 192.

[0102] In any of the above-described transmitter or receiverembodiments, when the subband signals are encoded waveforms such as CodeDivision Multiple Access (CDMA) or precision P(Y) GPS code signals, thesubband signals can be encoded or decoded to realize computationalsavings. In a receiver, for example, the subband signals are correlatedwith a replica of the transmitted signal prior to detection. Thecorrelation process can be performed before or after synthesis filteringor before conversion to digital (and therefore in analog) or afterconversion to digital (and therefore in digital). The approach isparticularly useful for the rapid, direct acquisition of widebandpseudorandom noise encoded waveforms, like CDMA type signals and theP(Y) GPS code, in a manner that is robust with respect to multipatheffects and wide-band noise. Because the M-subband signals have narrowbandwidths and therefore can be searched at slower rates, correlation ofthe subband signals rather than the signal or the composite signal canbe performed with over an M-fold reduction in computation and thereforereduce the individual component cost.

[0103] To provide further reductions in computational requirements, thenumber of subbands requiring correlation at any trial time and Dopplerfrequency can be reduced. The pseudorandom nature of the coded signalsimplies that a coded signal will only lie in certain known subbands atany given time. According to the rank-reduction principle and asillustrated by FIG. 13, subbands 200 a-j outside of the subbands 204 a-jcontaining the coded signal can be eliminated to reduce the effects ofwide-band noise in the acquisition and/or tracking of pseudorandomsignals. This is accomplished by eliminating any subband in which thenoise component exceeds the signal component (i.e., the SNR is less than1). Such an elimination increases the bias squared, which is the powerof the signal components that are eliminated, while drasticallydecreasing the variance, which is the power of the noise that waseliminated. In this manner, the mean squared error between the computedcorrelation function and the noise-free version of the correlationfunction is significantly reduced.

[0104] As shown in FIG. 14 to perform the correlation in the subbandsignals in GPS, CDMA, and other pseudorandom or random waveformapplications, the replicated code 208 from the code generator 212 mustbe passed through an analysis filter bank 216 that is identical to theanalysis filter bank 220 used to decompose the signal 224. Because thecorrelation must be performed for different segments of the replicatedcode 208, each indexed by some start time, this decomposition isnecessary for all trial segments of the replicated code 208. A pluralityof subband correlators 228 a-n receive both the subband signals 232 a-nand the replicated subband signals 236 a-n and generate a plurality ofsubband correlation signals 240 a-n. The subband correlation signals 240a-n are provided by the following equation:${q_{m,n}^{(i)}(j)} = {\sum\limits_{k = 1}^{N}{{x_{m}\left( {k + j} \right)}\quad {p_{n}^{(i)}(k)}}}$

[0105] where:

[0106] q(k) is the subband correlation signal;

[0107] p_(n) ^((i))(k) is the component of the i^(th) trial segment ofthe P(Y) code in the n^(th) subband;

[0108] x_(m)(k) is the component of the measurement that lies in them^(th) subband;

[0109] N is the number of samples over which the correlation isperformed.

[0110] The subband correlation signals 240 a-n are upsampled andinterpolated by the synthesis filters 244 a-n and then squared andcombined. The resulting composite signal 248 is the correlation functionthat can be further processed and detected.

[0111] After the subband correlation signals 240 a-n are generated, thesignals, for example, can be processed by a RAKE processor, which iscommonly a maximal SNR combiner, to align in both time and phasemultipath signals before detection and thereby provide improvedsignal-to-noise ratios and detection performance. As will beappreciated, a signal can be fragmented and arrive at a receiver viamultiple paths (i.e., multipath signals) due to reflections from otherobjects, particularly in urban areas. The formation of a number ofmultipath signals from a source signal can degrade the correlationpeaks, which contributes to the degradation of the detections. The RAKEprocessor determines the time and phase delays of these multipathsignals by searching for correlation peaks in the correlation functionand identifying the time and phase delays for each of the peaks. TheRAKE processor then uses the time and phase delay estimates to realignthe multipath signals so that they can add constructively and enhancethe correlation peaks. The peak enhancement improves detection becauseof the increase in signal-to-noise ratio.

[0112]FIG. 15 depicts an embodiment of a signal processing architectureincorporating these features. Referring to FIG. 11, the signals 300 arereceived by one or more antennas 304, down converted by a down converter308 to intermediate frequency, filtered by one or more filters 312, andpassed through an analog-to-digital converter 316 to form a digitalsignal 320. The digital signal 320 is passed through an analysis filterbank 324 to generate a plurality of subband signals 328 a-n, and thesubband signals 328 a-n to a plurality of subband correlators 332 a-n asnoted above to form a plurality of subband correlation signals 336 a-n.The subband correlation signals 336 a-n are passed to a synthesis filterbank 340 to form a correlation function 344 corresponding to the signal300. The correlation function 344 is passed to a pre-detector 348 todetermine an estimated transmit time and frequency and an amplitude anddelay for each of the correlation peaks. The estimated transmit time andfrequency 352 are provided to a code generator 356 and the amplitude andtime delay 360 associated with each correlation peak are provided to theRAKE processor 364. The code generator 356 determines a replicated code368 corresponding to the signal 300 based on the estimated trial timeand frequency. Using the correlation peak amplitudes and time and/orphase delays, the RAKE processor 364, as shown in FIG. 16, shifts theinput sequence y(k) by the amounts of the multipath time and/or phasedelays and then weights each shifted version by the amplitude of thepeak of the correlation function corresponding to that peak to form aRAKED signal 372 (denoted by y_(R)(k)). The RAKED sequence is commonlydefined by the following mathematical equation:${y_{R}(k)} = {\frac{1}{\sum\limits_{i = 1}^{p}A_{i}}{\sum\limits_{i = 1}^{p}{A_{i}^{{- j}\quad \varphi_{i}}{y\left( {k + t_{i}} \right)}}}}$

[0113] where:

[0114] p is the number of multipath signals (and therefore number ofpeaks);

[0115] A_(i) is the amplitude of the i^(th) peak;

[0116] t_(i) is the time delay of the i^(th) peak;

[0117] φ is the phase delay of the i^(th) peak;

[0118] y(k) is the input sequence into the code correlator.

[0119] The RAKED signal 372 and the replicated code 368 are correlatedin a correlator 376 to provide the actual transmit time and frequency380 which are then used by detector 384 to detect the signal.

[0120] There are a number of variations of the above-desc system. Thevariations are useful in specific applicat such as GPS, CDMA, and radar.

[0121] In one variation of the system of FIG. 15 that i depicted inFIGS. 17-18, multiplexed radar transmitte receiver architectures aredepicted. The radar signals 400 a-n are a number of coded waveforms thatoperate in separate, contiguous subbands (referred to as “radar susignals”). As shown in FIG. 17, the radar signals 40 are simultaneouslytransmitted by a plurality of transmitters 404 a-n that each include aplurality of analysis filters (not shown) to form the various radarsubband signals 400 a-n. Referring to FIG. 18, the va radar subbandsignals 400 a-n are received by a signal receptor 410 and passed througha plurality of bandpass filters 414 a-n. A bandpass filter 414 a-nhaving unique bandpass characteristics corresponds to each of the radarsubband signals. The various filtered subband signals 416 a-n aresampled by a plurality of decimators 422 a-n and quantized by aplurality of quantizers 426 a-n to form digital subband signals 430 a-n.The digital subband signals 430 a-n are analyzed by a plurality ofdetectors 434 a-n to form a corresponding plurality of detected signals438 a-n. The detectors 434 a-n use a differently coded waveform for eachof the transmitted radar subband signals 400 a-n so that the subbandradar signals can be individually separated upon reception. As notedabove in FIGS. 14-15, the coded radar waveform is decomposed by aplurality of analysis filters (not shown) that are identical to theanalysis filters in the receiver to provide replicated subband signalsto the detectors 434 a-n. Each detector 434 a-n correlates a radarsubband signal 430 a-n with its corresponding replicated subband signalto form a plurality of corresponding detected signals 438 a-n. Thedetected signals 438 a-n are analyzed by a synthesis filter bank 412 a-nto form a composite radar signal 446.

[0122] In a variation of the system of FIG. 15, a bank of analysisfilters and synthesis filters can be implemented both directly beforeand after the correlation step (not shown) to provide the above-notedreductions in computational requirements.

[0123] In another variation of the system of FIG. 15, the analysisfilters can be relocated before the analog-to-digital converter 316 toform the subband signals before as opposed to after conversion.

[0124] In another variation shown of the system of FIG. 15 that isdepicted in FIG. 20, the RAKE processor 364 can account for the relativedelays in antenna outputs of the signal 300 (which is a function of thearrangement of the antennas as well as the angular location of thesignal source) by summing the antenna outputs without compensating forthe relative output delays. The correlation process may result in N×ppeaks, where N is the number of antenna outputs and p is the number ofmultipath induced peaks. The Np peaks are then used to realign and scalethe input data before summation. The RAKE 364 in effect has performedthe phase-delay compensation usually done in beam-steering. Theadvantages of this approach compared to conventional beam steeringtechniques include that it is independent of antenna array geometriesand steering vectors, it does not require iterative searches fordirections as in LMS and its variants, and it is computationally veryefficient. This approach is discussed in detail in copending applicationhaving Ser. No. 08/916,884, and filed on Aug. 21, 1997.

[0125] While various embodiments of the present invention have beendescribed in detail, it is apparent that modifications and adaptationsof those embodiments will occur to those skilled in the art. However, itis to be expressly understood that such modifications and adaptationsare within the scope of the present invention, as set forth in thefollowing claims.

What is claimed is:
 1. A method for acquiring a signal having abandwidth, comprising: decomposing the signal into a plurality of signalsegments, each signal segment having a signal segment bandwidth that isless than the signal bandwidth; processing each of the signal segmentsto form a plurality of processed signal segments; and combining theprocessed signal segments into a composite signal wherein the signal isone of analog or digital and the composite signal is the other one ofanalog or digital.
 2. The method of claim 1 , wherein the processingstep includes performing analog-to-digital conversion of each of thesignal segments.
 3. The method of claim 1 , wherein the processing stepincludes performing digital-to-analog conversion of each of the signalsegments.
 4. The method of claim 1 , wherein the processing stepincludes removing a noise component from each of the signal segments toform a corresponding plurality of noise reduced signal segments andthereafter converting each of the noise reduced signal segments from oneof analog or digital format to the other of analog or digital format. 5.The method of claim 1 , wherein in the processing step each of thesignal segments is processed separately.
 6. The method of claim 1 ,wherein the composite signal has the same bandwidth as the signalbandwidth.
 7. The method of claim 1 , wherein the composite signal is atime delayed replica of the signal.
 8. The method of claim 1 , whereinthe signal has a bandwidth of at least about 1 GHz.
 9. The method ofclaim 1 , wherein the sum of the plurality of signal bandwidths isequivalent to the signal bandwidth.
 10. The method of claim 1 , whereinthe signal is in one of analog or digital format and the compositesignal is in the other of analog or digital format.
 11. The method ofclaim 1 , wherein the processing step comprises: assigning boundaryvalues to a plurality of bins; sampling a signal segment to provide asampled value corresponding to the sampled portion of the signalsegment; comparing the sampled value with assigned boundary values foreach of the plurality of bins; selecting an appropriate bin for thesampled portion of the signal segment; thereafter reassigning newboundary values to at least a portion of the plurality of bins; andrepeating the assigning, sampling, comparing and selecting steps. 12.The method of claim 1 , wherein the processing step comprises:correlating the plurality of signal segments with a correspondingplurality of replicated signal segments to provide a correspondingplurality of correlation functions.
 13. The method of claim 12 , whereinthe processing step comprises: determining an amplitude, time delay, andphase delay for at least a portion of a plurality of peaks defined bythe plurality of correlation functions and realigning and scaling atleast a portion of the signal defined by the signal segments based onone or more of the amplitude, time delay, and phase delay for the atleast a portion of the plurality of peaks.
 14. An apparatus foracquiring a signal having a signal bandwidth, comprising: means forreceiving a signal in the form pseudorandom or random waveform having asignal bandwidth; means for decomposing the signal into a plurality ofsignal segments, each signal segment having a signal segment bandwidththat is less than the signal bandwidth; means for processing each of thesignal segments to form a plurality of processed signal segments; andmeans for combining the processed signal segments into a compositesignal wherein the signal is one of analog or digital and the compositesignal is the other one of analog or digital.
 15. The apparatus of claim14 , wherein the means for processing includes means for performinganalog-to-digital conversion of each of the signal segments.
 16. Theapparatus of claim 14 , wherein the means for processing includes meansfor performing digital-to-analog conversion of each of the signalsegments.
 17. The apparatus of claim 14 , wherein the means fordecomposing is a plurality of low pass filters.
 18. The apparatus ofclaim 14 , wherein the means for decomposing includes a plurality ofanalysis filters and the means for combining includes a plurality ofsynthesis filters.
 19. The apparatus of claim 14 , wherein the means forcombining is a perfect reconstruction filter bank.
 20. The apparatus ofclaim 14 , wherein the means for processing includes at least one of aplurality of analog-to-digital converters and a plurality ofdigital-to-analog converters.
 21. The apparatus of claim 14 , whereinthe means for processing includes a noise rejecting quantizer.
 22. Amethod for reducing noise in a signal having a bandwidth, comprising:decomposing the signal into a plurality of signal segments, each signalsegment having a bandwidth that is less than the bandwidth of the signaland removing a noise component from each of the signal segments to forma corresponding plurality of processed signal segments.
 23. The methodof claim 22 , further comprising: combining each of the processed signalsegments to form a composite signal.
 24. The method of claim 23 ,wherein the composite signal has the same bandwidth as the signal.
 25. Asystem for reducing noise in a signal having a bandwidth, comprising:means for decomposing the signal into a plurality of signal segments,each signal segment having a bandwidth that is less than the bandwidthof the signal and means for removing a noise component from each of thesignal segments to form a corresponding plurality of processed signalsegments.
 26. The system of claim 25 , further comprising: means forcombining each of the processed signal segments to form a compositesignal.
 27. The system of claim 26 , wherein the composite signal hasthe same bandwidth as the signal.
 28. A method for combining a pluralityof signal segments having a signal bandwidth, to form a composite signalhaving a composite bandwidth, the frequency band of the composite signalincluding each of the signal segments, the method comprising: performingsynthesis filtering on each of the plurality of signal segments to formthe composite signal.
 29. The method of claim 28 , further comprising:emitting the plurality of signal segments from a plurality of signalsources and receiving each of the plurality of signal segments using acorresponding plurality of signal receptors.
 30. The method of claim 28, further comprising: converting each of the signal segments from ananalog format to a digital format.
 31. A system for assembling aplurality of signal segments, each having a signal bandwidth to form acomposite signal having a composite bandwidth that includes thefrequency range of each of the signal segments, the system comprising:means for performing synthesis filtering on each of the plurality ofsignal segments to form the composite signal.
 32. The system of claim 31, further comprising: means for emitting the plurality of signalsegments from a plurality of signal sources and means for receiving eachof the plurality of signal segments.
 33. The system of claim 31 ,further comprising: means for converting each of the signal segmentsfrom an analog format to a digital format.
 34. The system of claim 31 ,further comprising: a plurality of analysis filters to decompose asource signal into a plurality of decomposed signal segments; aplurality of digital-to-analog conversion devices for converting theplurality of decomposed signal segments from digital into analog formatto form a corresponding plurality of analog signal segments; a pluralityof amplifiers to form a corresponding plurality of signal segments; aplurality of signal emitters for emitting the plurality of signalsegments; and a plurality of receptors for receiving the plurality ofsignal segments.
 35. The system of claim 31 , further comprising: aplurality of analysis filters to decompose a source signal into aplurality of decomposed signal segments; a plurality of amplifiers toamplify the decomposed signal segments to form a corresponding pluralityof signal segments; a plurality of signal emitters for emitting theplurality of signal segments; and a plurality of receptors for receivingthe plurality of signal segments.
 36. The system of claim 31 , furthercomprising: a plurality of receptors for receiving a plurality of analogsignal segments; a plurality of analog-to-digital converters to convertthe plurality of analog signal segments into the plurality of signalsegments.
 37. A method for processing an analog signal having abandwidth, comprising: decomposing the analog signal into a plurality ofanalog signal segments, each analog signal segment having a signalsegment bandwidth that is less than the signal bandwidth and processingeach of the analog signal segments to form a plurality of processedanalog signal segments; and combining the processed analog signalsegments into a composite signal.